To integrate the function $\cosh(0x)$, we start by simplifying the expression.

Since $0x = 0$, we have:

$\cosh(0x) = \cosh(0)$

The value of $\cosh(0)$ is 1 because:

$\cosh(0) = \frac{e^0 + e^0}{2} = 1$

Thus, $\cosh(0x) = 1$. Now, integrating this constant:

$\int 1 \, dx = x + C$

where $C$ is the constant of integration.

Final Answer:

$\int \cosh(0x) \, dx = x + C$

Would you like a more detailed explanation or have any follow-up questions?

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Further Questions:

1. What is the definition of hyperbolic cosine (cosh)?
2. How do you integrate other hyperbolic functions like $\sinh(x)$ or $\cosh(x)$?
3. Can you explain the relationship between the hyperbolic functions and trigonometric functions?
4. How can you compute the derivative of $\cosh(x)$?
5. What is the significance of hyperbolic functions in physics and engineering?

Tip: Hyperbolic functions, such as $\cosh(x)$ and $\sinh(x)$, are closely related to exponential functions and can often simplify the analysis of certain problems, especially those involving differential equations.